CN114118296B - Rock mass structural plane dominant occurrence grouping method based on clustering integration - Google Patents
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Abstract
The invention relates to a method for grouping dominant occurrence of a rock mass structural plane based on clustering integration. The invention converts the structural surface attitude data acquired on site into corresponding space unit normal vector n= (x, y, z); calculating the distance D (n i,nj) between every two structural planes in the dataset to obtain a structural plane dataset distance matrix D N×N; m clustering is operated on the data set by adjusting a clustering algorithm or super parameters to obtain M differential base clustering results pi m; calculating a co-ordination matrix CA of the base clustering result; respectively setting the grouping number K as an integer not less than 2, and clustering the co-ordinates matrix CA by adopting a condensation hierarchical clustering algorithm; determining the optimal grouping number K op according to the clustering performance measurement index; and removing noise points and orphan values according to the clustering integration result of the optimal grouping number K op to obtain a structural face dominant-yield grouping result. The method can effectively identify the noise and the orphan value of the structural plane attitude data, and obtain a clustering effect better and more stable than that of a single clustering model.
Description
Technical Field
The invention relates to a clustering integration-based rock mass structural plane dominant occurrence grouping method, and belongs to the technical field of measurement and analysis of engineering geological survey structural planes.
Background
The structural surface is used as an important component of the rock mass, and influences and controls the mechanical property of the rock mass and the stability of the engineering structure to a great extent. The rock mass structural planes in the natural state have grouping characteristics, and the accurate and reliable structural plane dominant occurrence grouping has very important practical significance for rock mass strength parameter determination, mechanical characteristic research and engineering stability evaluation. In the process of structural plane measurement and statistical analysis, due to errors of measurement and recording and the existence of individual orphan structural planes, the dominant occurrence grouping result of the rock mass structural planes is often caused to be less ideal. At present, most of the cluster analysis methods mainly use a single cluster model, some assumptions made by the single cluster model on data do not necessarily accord with the real distribution situation of the data, local optimal solutions are easy to fall into, noise points and orphan values in the structural surface occurrence are difficult to identify, and accurate and effective clustering results are difficult to obtain. Therefore, a clustering integration technology is introduced, the essential characteristics of the data set are revealed from different levels by combining a plurality of base clustering results, the noise points and the orphan values of the structural surface are identified, and the defect of poor clustering effect of a single model is overcome.
Disclosure of Invention
Aiming at the problems that a single clustering model has larger misjudgment risk and is difficult to identify noise points and orphan values, the invention provides a clustering integration-based rock mass structural surface dominant occurrence grouping method, a plurality of differential base clustering results are constructed according to a given structural surface data set, and the clustering integration technology is utilized to integrate and complement information of the plurality of base clustering results so as to obtain a better and more robust clustering effect than the single clustering model.
A method for grouping dominant occurrence of rock mass structural planes based on clustering integration comprises the following specific steps:
(1) Converting the structural plane attitude data acquired on site into corresponding space unit normal vectors n= (x, y, z);
(2) Calculating the distance D (n i,nj) between every two structural planes in the dataset to obtain a structural plane dataset distance matrix D N×N;
(3) M clustering is operated on the data set by adjusting a clustering algorithm or super parameters to obtain M differential base clustering results pi m;
(4) Calculating a co-ordination matrix CA of the base clustering result;
(5) Respectively setting the grouping number K as an integer not less than 2, and clustering the co-ordinates matrix CA by adopting a condensation hierarchical clustering algorithm;
(6) Determining the optimal grouping number K op according to the clustering performance measurement index;
(7) And removing noise points and orphan values according to the clustering integration result of the optimal grouping number K op to obtain a structural face dominant-yield grouping result.
The structural plane shape acquired in the step (1) is expressed by adopting a trend alpha and an inclination angle beta, and the structural plane shape is converted into a space unit normal vector n= (x, y, z) form with the following calculation formula:
The distance D (n i,nj) in the step (2) is a sine value of a unit normal vector included angle of the two structural surfaces, and the distance D (n i,nj) of the unit normal vector n i(xi,yi,zi)、nj(xj,yj,zj of the two structural surfaces is as follows:
Wherein n i and n j respectively represent unit normal vectors of the structural planes i and j, θ represents an included angle of the unit normal vectors of the two structural planes, and T is a transposed symbol of the matrix.
The clustering algorithm in the step (3) is a K-means based on division, a hierarchical aggregation hierarchical clustering based on hierarchy, a DBSCAN based on density or a graph-based spectral clustering algorithm.
The super-parameters are parameters set by a clustering algorithm during cluster analysis, each clustering algorithm comprises a plurality of super-parameters, for example, K-means, aggregation level clustering and spectral clustering algorithms comprise a grouping number K, and a DBSCAN algorithm comprises a radius eps and a minimum sample number min_samples;
From the clustering algorithm perspective, the method for generating the base clustering result with differentiation comprises the following steps: using the same clustering algorithm, setting different super parameters to cluster the data set to generate a base clustering result; for example, K-means, hierarchical aggregation and spectral clustering algorithms can set the K value to be an integer not less than 2; the DBSCAN algorithm can set the radius eps to be 0.1-0.3, the minimum sample number min_samples can be set to be 2-10, and according to the data set density, the larger the density is, the larger the min_samples are, and the smaller the eps is;
from the perspective of a clustering algorithm, the method for generating the base clustering result with differentiation can also use different clustering algorithms to cluster the data set to generate the base clustering result; the two methods can also be combined to generate a base clustering result;
The step (4) is to reorganize the base clustering result, avoid the corresponding problem of the group labels in the base clustering result, and measure the similarity between the data points digitally and accurately; the co-ordinates matrix CA calculation expression is:
CA＝{mij}N×N
wherein N is the data quantity of the structural plane,
Pi m(xi) is the group to which the sample x i belongs in the base cluster result pi m,For whether samples i and j are present in the same group, if samples i and j are present in the same group/>Otherwise/>The larger the frequency of dividing a certain structural surface into the same group by the base clustering result is, the larger the corresponding CA element value is.
The aggregation hierarchical clustering algorithm in the step (5) is as follows
Each sample in the CA matrix is taken as a separate group, and during each iteration, the two highest frequency groups divided into the same group are combined into one group step by step until a termination condition is reached or finally grouped into one group.
The clustering performance measurement index in the step (6) indicates an index for measuring the clustering effect of the structural surface occurrence data, the contour coefficient SC is adopted as the clustering performance measurement index, and the SC expression is that
Where s (i) denotes the profile factor of a sample,
A (i) represents the average distance between sample x i and the other samples of the same group, and b (i) represents the average distance between sample x i and all samples of the nearest neighbor group;
The SC value range is [ -1,1], and the larger the SC value is, the better the clustering effect is;
And (3) the optimal grouping number K op in the step (6) refers to the grouping number K value with the largest corresponding clustering performance measurement index profile coefficient.
And (7) noise and orphan values in the step are obtained by dividing the base clustering result in the clustering integrated model into the same group of structural surfaces with very low frequency.
The beneficial effects of the invention are as follows:
(1) The invention introduces a clustering integration technology to realize the transition from a single clustering model of a traditional structural plane to an integration model;
(2) According to the invention, through integrating and complementing a plurality of basic clustering results, the defects that the conventional single clustering model has misjudgment risk, is difficult to identify noise points and orphan values and is easy to fall into a local optimal solution are overcome, the structure face occurrence clustering effect is improved, the clustering result has a global meaning, an effective method is provided for the correct grouping of the dominant occurrence of the rock mass structure face, and the method can be widely applied to structure face statistical analysis in industries such as water conservancy and hydropower, mine, road construction and the like.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic view of the angles of the unit normal vectors of the structural plane space;
FIG. 3 is a plot of the production poles of a structural face of a cone hydropower station dam foundation;
FIG. 4 illustrates the contour coefficients of the clustering integrated model corresponding to different grouping numbers K;
FIG. 5 is a clustering integration result of structural plane morphology;
Fig. 6 is a structural plane dominance grouping result.
Detailed Description
The invention will be described in further detail with reference to specific embodiments, but the scope of the invention is not limited to the description.
Example 1: as shown in fig. 1, a clustering integration-based rock mass structural plane dominant occurrence grouping method specifically comprises the following steps:
(1) Converting the structural plane attitude data acquired on site into corresponding space unit normal vectors n= (x, y, z);
the structure surface morphology acquired on site is expressed by adopting a trend alpha and an inclination angle beta, and the structure surface morphology is converted into a space unit normal vector n= (x, y, z) form with the following calculation formula:
(2) Calculating the distance D (n i,nj) between every two structural planes in the dataset to obtain a structural plane dataset distance matrix D N×N;
The distance D (n i,nj) is a sine value of the unit normal vector included angle of the two structural surfaces, the schematic diagram of the unit normal vector included angle of the structural surfaces is shown in fig. 2, and the distance D (n i,nj) of the unit normal vector n i(xi,yi,zi)、nj(xj,yj,zj of the two structural surfaces is as follows:
Wherein n i and n j respectively represent unit normal vectors of structural planes i and j, θ represents an included angle of the unit normal vectors of the two structural planes, and T is a transposed symbol of the matrix;
(3) M clustering is operated on the data set by adjusting a clustering algorithm or super parameters to obtain M differential base clustering results pi m;
The clustering algorithm is K-means based on division, aggregation hierarchical clustering based on hierarchy, DBSCAN based on density or spectral clustering algorithm based on graph; the super-parameters are parameters set by a clustering algorithm during cluster analysis, each clustering algorithm comprises a plurality of super-parameters, for example, K-means, aggregation level clustering and spectral clustering algorithms comprise a grouping number K, and a DBSCAN algorithm comprises a radius eps and a minimum sample number min_samples;
From the clustering algorithm perspective, the method for generating the base clustering result with differentiation comprises the following steps: using the same clustering algorithm, setting different super parameters to cluster the data set to generate a base clustering result; for example, K-means, hierarchical aggregation and spectral clustering algorithms can set the K value to be an integer not less than 2; the DBSCAN algorithm can set the radius eps to be 0.1-0.3, the minimum sample number min_samples can be set to be 2-10, and according to the data set density, the larger the density is, the larger the min_samples are, and the smaller the eps is;
from the perspective of a clustering algorithm, the method for generating the base clustering result with differentiation can also use different clustering algorithms to cluster the data set to generate the base clustering result; the two methods can also be combined to generate a base clustering result;
(4) Calculating a co-ordination matrix CA of the base clustering result;
The co-ordination matrix CA is used for reorganizing the base clustering result, avoiding the corresponding problem of the group labels in the base clustering result, and measuring the similarity between data points in a digitalized and accurate manner; the co-ordinates matrix CA calculation expression is:
CA＝{mij}N×N
wherein N is the data quantity of the structural plane,
Pi m(xi) is the group to which the sample x i belongs in the base cluster result pi m,For whether samples i and j are present in the same group, if samples i and j are present in the same group/>Otherwise/>The larger the frequency of dividing a certain structural surface into the same group by the base clustering result is, the larger the corresponding CA element value is;
(5) Respectively setting the grouping number K as an integer not less than 2, and clustering the co-ordinates matrix CA by adopting a condensation hierarchical clustering algorithm;
the aggregation hierarchical clustering algorithm is
Taking each sample in the CA matrix as a single group, gradually combining two highest combinations divided into the same group frequency into one group in each iteration process until a termination condition is reached or finally grouping into one group;
(6) Determining the optimal grouping number K op according to the clustering performance measurement index;
The clustering performance measurement index refers to an index for measuring the clustering effect of structural surface occurrence data, the contour coefficient SC is adopted as the clustering performance measurement index, and the SC expression is that
Where s (i) denotes the profile factor of a sample,
A (i) represents the average distance between sample x i and the other samples of the same group, and b (i) represents the average distance between sample x i and all samples of the nearest neighbor group;
The SC value range is [ -1,1], and the larger the SC value is, the better the clustering effect is;
the optimal grouping number K op is the grouping number K value with the largest profile coefficient corresponding to the clustering performance measurement index;
(7) Removing noise points and orphan values according to the clustering integration result of the optimal grouping number K op to obtain a structural face dominant-yield grouping result; the noise points and the orphan values refer to that the base clustering result in the clustering integrated model is divided into the same group of structural surfaces with very low frequency.
Example 2: as shown in fig. 1, a clustering integration-based rock mass structural plane dominant occurrence grouping method specifically comprises the following steps:
(1) The structural surface attitude data of the cone hydropower station dam foundation-footrill investigation are used as test data, and a structural surface attitude polar diagram is shown in figure 3 and comprises 305 structural surfaces; converting its occurrence into a spatial unit normal vector n= (x, y, z):
(2) Calculating the distance D (n i,nj) of every two structural planes by using the sine value of the included angle of the space unit normal vector, wherein the schematic diagram of the included angle of the unit normal vector of the structural plane is shown in fig. 2, and constructing a distance matrix D N×N of the structural plane data set;
Wherein n i and n j respectively represent unit normal vectors of structural planes i and j, θ represents an included angle of the unit normal vectors of the two structural planes, and T is a transposed symbol of the matrix;
(3) Taking K-means as an example, aiming at a structural surface occurrence dataset, carrying out disturbance by adjusting the super-parameter K value of the K-means, wherein the K value is an integer of 2-11, and 10 differential base clustering results are obtained;
(4) Reorganizing 10 base clustering results, calculating a co-ordination matrix CA of the base clustering results, avoiding the corresponding problem of group labels in the base clustering results, and measuring the similarity between data points in a digitalized and accurate manner;
The CA calculation expression is:
CA＝{mij}N×N
Where N represents the number of structural plane shape data, n=305, Pi m(xi) represents the group to which sample x i belongs in the base cluster result pi m,/>Indicating whether samples i and j are present in the same group, if a pair of samples i, j are present in the same group,/>Otherwise/>The larger the frequency of dividing a certain structural surface into the same group by the base clustering result is, the larger the corresponding CA element value is;
(5) And respectively setting the grouping number K as an integer of 2-10, and clustering the co-ordinates matrix CA by adopting a condensation hierarchical clustering algorithm.
Taking each sample in the CA matrix as a single group, gradually combining two highest combinations divided into the same group frequency into one group in each iteration process until reaching a termination condition or finally grouping into one group;
(6) Calculating a clustering performance metric index profile coefficient SC of a CA matrix of each algorithm in the grouping number K epsilon [2, 10], wherein the SC expression is as shown in figure 4:
where s (i) represents the contour coefficient of one of the samples, A (i) represents the average distance between sample x i and the other samples of the same group; b (i) represents the average distance between sample x i and all samples of the nearest neighbor set;
As can be seen from fig. 4, the clustering performance metric index SC is the largest and the clustering effect is the best when k=4 by the 4 clustering algorithms, so the optimal grouping number K op of the structural plane dataset is determined to be 4;
(7) According to the optimal grouping number K op, a final clustering integration result is obtained, as shown in fig. 5, the structural surface with the identifier of 'X' is very dispersed, and no grouping occurs, so that the structural surface of the group is noise and solitary value;
(8) After noise points and orphan values are removed, the structure face data dominant-yield grouping result is shown in fig. 6, and the fact that the footrill has 3 groups of dominant structure faces is known, and the grouping result is consistent with the actual situation;
Comparing the clustering effects before and after the integration, wherein the maximum value of SC in 10K-means clustering models before the clustering integration is 0.16; after clustering integration and noise and orphan value elimination, sc=0.60, the clustering effect is remarkably improved, and the clustering integration technology is feasible and effective when applied to structure face dominant grouping, so that clear inter-group boundaries are provided, noise and orphan value structure faces are effectively marked, and the method is difficult to realize by a common structure face dominant grouping method.
While the present invention has been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (8)
1. The method for grouping the dominant occurrence of the rock mass structural plane based on clustering integration is characterized by comprising the following specific steps of:
(1) Converting the structural plane attitude data acquired on site into corresponding space unit normal vectors n= (x, y, z);
(2) Calculating the distance D (n i,nj) between every two structural planes in the dataset to obtain a structural plane dataset distance matrix D N×N;
(3) M clustering is operated on the data set by adjusting a clustering algorithm or super parameters to obtain M differential base clustering results pi m;
(4) Calculating a co-ordination matrix CA of the base clustering result;
(5) Respectively setting the grouping number K as an integer not less than 2, and clustering the co-ordinates matrix CA by adopting a condensation hierarchical clustering algorithm;
(6) Determining the optimal grouping number K op according to the clustering performance measurement index;
(7) And removing noise points and orphan values according to the clustering integration result of the optimal grouping number K op to obtain a structural face dominant-yield grouping result.
2. The clustering integration-based rock mass structural plane dominance attitude grouping method according to claim 1, wherein: the structural plane shape acquired in the step (1) is expressed by adopting a trend alpha and an inclination angle beta, and the structural plane shape is converted into a space unit normal vector n= (x, y, z) form with the following calculation formula:
3. The clustering integration-based rock mass structural plane dominance attitude grouping method according to claim 1, wherein: step (2) is that the distance D (n i,nj) is the sine value of the unit normal vector included angle of the two structural surfaces, and the distance D (n i,nj) of the unit normal vector n i(xi,yi,zi)、nj(xj,yj,zj of the two structural surfaces:
Wherein n i and n j respectively represent unit normal vectors of the structural planes i and j, θ represents an included angle of the unit normal vectors of the two structural planes, and T is a transposed symbol of the matrix.
4. The clustering integration-based rock mass structural plane dominance attitude grouping method according to claim 1, wherein: the clustering algorithm in the step (3) is K-means based on division, aggregation hierarchical clustering based on hierarchy, DBSCAN based on density or spectral clustering algorithm based on graph.
5. The clustering integration-based rock mass structural plane dominance attitude grouping method of claim 4, wherein: the super-parameters are parameters set by a clustering algorithm during cluster analysis.
6. The clustering integration-based rock mass structural plane dominance attitude grouping method according to claim 1, wherein: the calculation expression of the co-ordination matrix CA in the step (4) is as follows:
CA＝{mij}N×N
wherein N is the data quantity of the structural plane,
Pi m(xi) is the group to which the sample x i belongs in the base cluster result pi m,For whether samples i and j are present in the same group, if samples i and j are present in the same group/>Otherwise/>
7. The clustering integration-based rock mass structural plane dominance attitude grouping method according to claim 1, wherein: the aggregation hierarchical clustering algorithm in the step (5) is that
Each sample in the CA matrix is taken as a separate group, and during each iteration, the two highest frequency groups divided into the same group are combined into one group step by step until a termination condition is reached or finally grouped into one group.
8. The clustering integration-based rock mass structural plane dominance attitude grouping method according to claim 1, wherein: the clustering performance measurement index in the step (6) adopts a contour coefficient SC, and the SC expression is
Where s (i) denotes the profile factor of a sample,
A (i) represents the average distance between sample x i and the other samples of the same group, and b (i) represents the average distance between sample x i and all samples of the nearest neighbor group.
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